30 research outputs found
Generalized Majority-Minority Operations are Tractable
Generalized majority-minority (GMM) operations are introduced as a common
generalization of near unanimity operations and Mal'tsev operations on finite
sets. We show that every instance of the constraint satisfaction problem (CSP),
where all constraint relations are invariant under a (fixed) GMM operation, is
solvable in polynomial time. This constitutes one of the largest tractable
cases of the CSP
The subpower membership problem of 2-nilpotent algebras
The subpower membership problem SMP(A) of a finite algebraic structure A asks
whether a given partial function from A^k to A can be interpolated by a term
operation of A, or not. While this problem can be EXPTIME-complete in general,
Willard asked whether it is always solvable in polynomial time if A is a
Mal'tsev algebras. In particular, this includes many important structures
studied in abstract algebra, such as groups, quasigroups, rings, Boolean
algebras. In this paper we give an affirmative answer to Willard's question for
a big class of 2-nilpotent Mal'tsev algebras. We furthermore develop tools that
might be essential in answering the question for general nilpotent Mal'tsev
algebras in the future.Comment: 17 pages (including appendix
MAL’TSEV CONDITIONS, LACK OF ABSORPTION, AND SOLVABILITY
Abstract. We provide a new characterization of several Mal’tsev conditions for locally finite varieties using hereditary term properties. We show a particular example how lack of absorption causes collapse in the Mal’tsev hierarchy, and point out a connection between solvability and lack of absorption. As a consequence, we provide a new and conceptually simple proof of a result of Hobby and McKenzie, saying that locally finite varieties with a Taylor term possess a term which is Mal’tsev on blocks of every solvable congruence in every finite algebra in the variety. 1
Logic and Automata
Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field